Hadronic models of blazars require a change of the accretion paradigm

0.12 MB·English

by  Andrzej A. Zdziarski

Mon.Not.R.Astron.Soc.000,1–6(2015) Printed6March2015 (MNLATEXstylefilev2.2)
Hadronic models of blazars require a change of the accretion
paradigm
Andrzej A. Zdziarski1 and Markus Bo¨ttcher2,3
5 1CentrumAstronomiczneim.M.Kopernika,Bartycka18,PL-00-716Warszawa,Poland
1 2CentreforSpaceResearch,North-WestUniversity,Potchefstroom2520,SouthAfrica
0 3AstrophysicalInstitute,DepartmentofPhysicsandAstronomy,OhioUniversity,Athens,OH45701,USA
2

r
a Accepted2015March5.Received2015March3;inoriginalform2015January24
M

5 ABSTRACT
Westudyhadronicmodelsofbroad-bandemissionofjetsinradio-loudactivegalacticnuclei,

] andtheirimplicationsfortheaccretioninthosesources.Weshowthatthemodelsthataccount
E
for broad-band spectra of blazars emitting in the GeV range in the sample of Bo¨ttcher et
H
al. have highly super-Eddington jet powers. Furthermore, the ratio of the jet power to the
. radiativeluminosityoftheaccretiondiscis 3000onaverageandcanbeashighas 105.
h
∼ ∼
p Wethenshowthatthemeasurementsoftheradiocoreshiftforthesampleimplylowmagnetic
- fluxesthreadingtheblackhole,whichrulesouttheBlandford-Znajekmechanismtoproduce
o powerfuljets. These results require that the accretion rate necessary to power the modelled
r jets is extremelyhigh, and the averageradiativeaccretion efficiencyis 4 10 5. Thus, if
t −
s the hadronic model is correct, the currently prevailing picture of accre∼tion×in AGNs needs
a
tobesignificantlyrevised.Also,theobtainedaccretionmodecannotbedominantduringthe
[
lifetimesof the sources, as the modelledveryhigh accretionrates wouldresult in too rapid

2 growthofthecentralsupermassiveblackholes.Finally,theextremejetpowersinthehadronic
v modelareinconflictwiththeestimatesofthejetpowerbyothermethods.
4
2 Keywords: accelerationofparticles–galaxies:active–galaxies:jets–ISM:jetsandoutflows–
1 quasars:general–radiationmechanisms:non-thermal.
6
0
.
1
0
1 INTRODUCTION efficiently.Still,thosehadronsintheleptonicmodelsusuallydom-
5
inatethekineticluminosityofjets(e.g.,Ghisellinietal.2014).
1
: The most commonly considered models of broad-band emission Sikoraetal. (2009) and Sikora (2011) have shown that the
v ofradio-loudjetsinAGNsutilizeemissionofrelativisticelectrons hadronicprocessesareveryinefficient.Thisimpliesthat,iftheto-
i
X andpositronsviasynchrotronandComptonprocesses.Theselep- taljetpowerisapproximatelylimitedbytheEddingtonluminosity,
tonicmodelshavebeenhighlysuccessfulinreproducingthespec- thehadronicmodel canberuledout inmanycases. Ontheother
r
a traandtimevariabilityofblazarsandradiogalaxies,thoughthere hand, Bo¨ttcheretal.(2013)(hereafterB13) havesuccessfully ap-
aresomephenomena,suchastheirextremelyshortvariabilitytime pliedhadronicmodelstoasampleofradio-loudAGNscircumvent-
scales,insomecasesdowntoafewminutes(Aharonianetal.2007; ing this constraint by allowing the jet power to be highly super-
Albertetal.2007),thatarenotreadilyexplainedbythem. Eddington.Herewediscussconsequencesofthissupposition.
Thealternative,andquitepopular,modelisbasedonhadronic
(or lepto-hadronic) processes (e.g.,Mannheim&Biermann1992;
Mu¨cke&Protheroe2001;Aharonian2000).Itutilizesemissionof 2 ANALYSISOFTHESAMPLEOFB13
extremely relativistic ions, mainly due to proton-synchrotron and
Westudyherethesampleof12blazarsofB13.Theirbroad-band
photo-pionproductionprocesses,toexplainthehigh-energyemis-
spectrawerefittedbythembyleptonicandhadronicmodels,and
sionfromjet-dominatedAGNs.Thelatterprocessgivesrisetocas-
weconsiderherethejetpowersobtainedbyB13forthelatter.B13
cadesofelectronsandpositrons,alsoemittingviathesynchrotron
provide the redshifts, z, the apparent superluminal velocity, β ,
andComptonprocesses.Thepeakofthehigh-energyemissionof app
andtheaccretionluminosity,L ,seeTable1.Sixofthoseobjects
thebroadbandspectralenergydistributionofblazars,at 0.1–10 acc
∼ werealsopresentinthesampleofZamaninasabetal.(2014)(here-
GeV,isthenduetotheseprocesses,mostlyprotonsynchrotron.
after ZCST14), for which those authors provide estimates of the
Westressthatthename’hadronic’refersonlytotheemission black-holemass, M,β ,and L basedonliterature.Thevalues
app acc
processes,andthe’leptonic’jetsinAGNmodelsalsocontainions, ofβ agreewellbetweenZCST14andB13,whilethevaluesof
app
thoughwithrelativelylowenergies,preventingthemfromradiating L agreetowithinafactor of 2,which isasatisfactory agree-
acc ∼
c 2015RAS
(cid:13)
2 A. A. Zdziarski& M. Bo¨ttcher
3.0
1.0
2.5
PL@(cid:144)DlgjE 112...050 @DΦlgBH 00..05
-0.5
0.5
a
0.0 -1.0
-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
lg@Lacc(cid:144)LED lg@Lacc(cid:144)LED
5.0
Figure2.Thedimensionless magnetic fluxφBH asafunction oftheEd-
4.5 dingtonratio.ThedashedlineshowthegeometricaverageofφBH 1.9.
4.0 Themodelofefficientjetformationviablack-holespinenergyextr≃action
LDacc 3.5 (Blandford&Znajek1977)predictφBH > 50(Tchekhovskoyetal.2011;
P@(cid:144)gj 3.0 McKinneyetal.2012),whichismuchhig∼herthantheobtainedvalues.
l
2.5
2.0 b
equation of state can be described by an adiabatic index of 4/3),
1.5
-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 seeTable1.Weneglectapossiblecontributionofcoldprotons,and
lg@Lacc(cid:144)LED consideronlythoseinthepower-lawdistributionassumedtogive
risetotheobserved spectrum, following thefitsofB13. Wethen
Figure1.Theratioofthetotaljetpowerto(a)theEddingtonluminosity
compareP tobothL (calculatedforanHfractionofX=0.7)and
and(b)theaccretion luminosityasfunctions oftheEddingtonratio.The j E
L inFig.1. Wefind P/L 85, P/L 2660, withthe
dashedlinesshowthegeometricaverages. acc h j Ei ≃ h j acci ≃
standarddeviationscorresponding tofactorsof 10and 8.4,re-
≃ ≃
spectively.(Hereafterthesymbol . denotesageometricaverage,
hi
mentgiventhenecessaryapproximatecharacterofthoseestimates. i.e.,averageoflogarithms,andthegivenstandarddeviationcorre-
However, theexception isW Comae, for which the L estimate spondstoamultiplicativefactor.)ExceptforWComaeandOJ287,
acc
usedbyB13is40timeshigherthanthatgiveninZCST14,which thedistributionof Pj/LE isrelativelyuniform.Asaconsequence,
is the upper limit of Ghisellinietal. (2010), hereafter G10. B13 thereisananti-correlationbetweenPj/LaccandLacc/LE,butallthe
usedtheestimateofXieetal.(2008),whoreferinturntotwoother obtainedvaluesarestillveryhigh,spanningPj/Lacc∼50–105.Fur-
papers,whichdonotseemtogivethatinformation.Thus,weuse thermore,someofourvaluesofLaccareupperlimits,andthecor-
herethevalueofG10.B13quoteanestimateof Lacc ofXieetal. respondingtruevaluesofPj/Lacccanbeevenhigher.
(2008)forOJ287,whichis7timeshigherthantheupperlimitof In general, we can write Pj = ǫjM˙c2, where M˙ is
G10;hereweusethelatter.Fortwoobjects(S50716+714and3C the accretion rate and ǫj < 1.5, the ratio of the jet
66A), B13giveno estimatesof L , andweusetheupper limits power to the available accreti∼on power, which we will call
acc
givenbyG10.Inthecaseof3C66A,thereisalsoanuncertainty here the jet formation efficiency. The approximate maxi-
ofitsredshift,andB13usedanestimatedredshiftofz=0.3based mum corresponds (Tchekhovskoy,Narayan&McKinney 2011;
onEBL-correctedSEDmodelling(Abdoetal.2011),whichisalso McKinney,Tchekhovskoy&Blandford 2012) to efficient extrac-
marginallyconsistentwiththespectroscopicallydeterminedlower tionof theblack-hole spin energy (Blandford&Znajek1977),in
limitontheredshiftbyFurnissetal.(2013).Sinceweusetheesti- which case the jet power may exceed M˙c2. However, attaining
matesofthejetpowerfromB13,weadopttheirredshiftvalueand such a high jet formation efficiency requires the accretion flow
rescaletheupperlimitofL ofG10,whousedz= 0.444,bythe to possess a strong poloidal magnetic field (Tchekhovskoyetal.
acc
ratioof D2, where D isthe luminosity distance. We assume the 2011; McKinneyetal. 2012), namely to form a magnetically ar-
L L
samecosmological parameters asB13, Ω = 0.7, Ω = 0.3 and rested disc(MAD, Narayan,Igumenshchev&Abramowicz 2003;
Λ m
H =70km/(s Mpc). see also Bisnovatyi-Kogan&Ruzmaikin 1976). The required en-
0
FortheobjectsnotinthesampleofZCST14,wefindmasses- ergy density corresponds then to the magnetic flux threading a
timatesfromtheliterature,inparticularfromG10.Insomecases, rapidlyspinningblackholeofΦBH =φBH(M˙c)1/2rg,withφBH ≃50,
thereisaconsiderableuncertainty.ForOJ287,weuse6.2 108M whichcorrespondstothemagneticfieldstrengthatthehorizonof
fromWang,Luo&Ho(2004).However,ifthesystemis×indeed⊙a B2/8π ∼ 100m˙mpc2/(σTrg),where m˙ = M˙c2/LE,rg = GM/c2 is
binary black-hole system, the massof the lessand more massive thegravitationalradius,mpistheprotonmass,andσTistheThom-
component is estimated as 1.4 108M and 1.8 1010M , re- soncrosssection.Sincethemagneticfluxisconserved inthejet,
spectively (Valtonen,Ciprini&×Lehto 20⊙12). Accre×tion wou⊙ld be itcanbemeasuredatlargescales,e.g.,throughtheradio-coreshift
dominatedbythemoremassiveblackhole.Theadoptedvaluesof effect (Lobanov 1998; Hirotani 2005). Values of φBH ∼ 50 were
L andMforallsourcesstudiedherearegiveninTable1. foundforalargesampleofblazarsandradiogalaxiesbyZCST14
acc
B13givethejetpower1estimatedusingtheenergycontentand assuming M˙c2 = Lacc/ǫr fortheiradoptedaccretionradiativeeffi-
fPor,oisnethjeeteonnthlya,lpsyeefltuhxeir(ee.qgu.,atLioenvsin(s3o–n5)2.0H06o)w,eavnedr,tthheecjeotupnotewrjeert, mcieondceylooffBǫr1=3,0w.4e.hHavoweetoveers,tgimivaetnetMh˙atinPsjte≫adLfraoccminththeejehtapdorowneirc,
j
should beincluded intheenergy budget. Thus,wemultiply their stronglydominatingtheenergybudget,i.e.,M˙c2 ≃Pj/ǫj≫Lacc/ǫr.
valuesby8/3,assumingtheprotonsarerelativistic(andthustheir TocalculatethevaluesofφBHimpliedbythehadronicmodel,
we use the radio core shift, ∆θ, measurements between 8 and 15
GHz for the sources in our sample from Pushkarevetal. (2012),
1 TheentryforLp (thepowerinprotons)ofOJ287inB13isatypo,it whichwegiveinTable1.WeapplyacorrectionofZdziarskietal.
shouldbe0.083ratherthan8.3. (2015)tothepowerofthe(1+z)factorintheformulaforthemag-
c 2015RAS,MNRAS000,1–6
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Hadronicmodelsof blazars 3
Table1.Themainparametersofthesample.FSRQ-flatspectrumradioquasar,LBL,IBLandHBLrefertoblazarswhichsynchrotronspectrumhasthepeak
atlow,intermediateandhighfrequencies,respectively;νandνFνgivetheestimatedpositionofthepeakoftheGeVspectrumapproximatedasapowerlaw,
andPjisthetotaljet+counterjetpowerinthehadronicmodelofB13.SeeB13fortheremainingparametersofthesources.
Object type z Lacc M Lacc/LE ∆θ ν νFν γmin γmax Pj
ergs−1 M mas 1022Hz 10−10ergcm−2s−1 109 1048ergs−1
⊙
00223159++146248((A3CO)66A) LIBBLL 00.9.34 34..4800×11004434 44×110088 8.01.×001507−4 00..007036 1300 17 11 14..23 32.72
0420-014(PKS) FSRQ 0.914 3.02×1046 2.5×7 108 0.97 0.256 5 1 103 0.43 1.4
0528+134(PKS) FSRQ 2.07 1.70×1047 1.07×109 1.07 0.150 5 2 1 1.1 117
0716+714(S5) LBL 0.31 1.80×1044 1 ×108 0.012 0.125 70 1 1 2.7 0.69
0851+202(OJ287) LBL 0.306 1.50×1044 6.2× 108 0.0016 0.051 5 0.5 1 1.0 0.23
1219+285(WComae) IBL 0.102 1.50×1043 5 ×108 2.0 10 4 0.047 80 0.5 1 1.9 0.059
1226-023(3C273) FSRQ 0.158 1.30×1047 6.5×9 109 0×.13− 0.017 2 10 103 0.43 67
1253-055(3C279) FSRQ 0.536 2.00×1045 8 ×108 0.017 0.051 10 1 103 0.63 9.3
1510-089(PKS) FSRQ 0.36 1.12×1046 1.5×8 108 0.48 0.151 8 5 103 1,1 6.7
2200+420(BLLac) LBL 0.069 1.51×1045 1.70×108 0.060 0.052 10 0.3 1 1.9 26
2251+058(3C454.3) FSRQ 0.859 7.24×1046 4.90×108 1.00 0.159 10 10 103 1.1 96
× ×
neticfieldstrengthat1pc,B ,andthenusetheformulaforthejet tribution,andassumethejetLorentzfactor,Γ,tobeone-halfofthe
1
magneticflux,Φ,ofequation(5)ofZCST14.FromΦ =Φ we Dopplerfactor,δ,whileΓ=δfortheinclinationanglei=1/Γ,as
j j BH
obtainφ ,whichweplotinFig.2forǫ = 1andthedimension- favouredonstatisticalgrounds.Thus,forcomparisonwiththere-
BH j
lessblack-holeangularmomentumof1.Wefind φ 1.9with sultshere,theirjetpowersneedtobemultipliedbyafactorof32/3.
h BHi≃
thestandarddeviationofa(multiplicative)factorof 5.Thesere- Still,wedonotexcludethatasub-Eddingtonjetpowerscanbeob-
≃
sultcanbecomparedtoanotherformulaforΦ ofZdziarskietal. tainedforsomeobjects,asitis,e.g.,thecaseforWComaeinour
j
(2015),whichtakesintoaccounteffectsduetothesmalljetopening sample.Generally,duetothesubstantiallylowertotalluminosities
anglesintheradio-emittingregion(andtheconsequent lowvalue andatleastequallylarge(ifnotlarger)black-holemassesofHBLs
of the magnetization parameter), and due to transverse averaging comparedtolow-frequencypeakedblazars(especiallyFSRQs),it
ofthemagneticfield.Thatformulayieldsvalueslowerbyapproxi- seems less problematic to produce hadronic model fits with sub-
mately √2fromthoseabove.Thus,ourresultsappeartogiverobust EddingtonjetpowersforHBLs.
approximateestimatesofthemagneticflux(undertheassumption
of the hadronic jet model). Given this and that all objects in the
samplehaveφ 50,wecanruleouttheefficientversionofthe
BH ≪ 3 THEMINIMUMJETPOWERINTHE
modelofBlandford&Znajek(1977)forthesample.(Wenotethat
PROTON-SYNCHROTRONMODEL
thismodelislikelytoworkforthestudiedsourcesiftheleptonic
modelisadopted,asinZCST14.) Theaboveresultsareforthemodel fitsofB13which,duetothe
Inotherjetformationmodels(e.g.,Blandford&Payne1982; largenumberofparameters,maygenerallynotbetheonlypossible
Coughlin&Begelman 2014), the jet formation efficiency has to hadronicmodelrepresentationofthechosenSEDs.Wemaythere-
be < 1, and it is usually ǫ 1. Thus, the accretion pro- fore ask whether another set of fits of the hadronic model could
j ≪
cess is even more highly super-Eddington. For such accretion, have lower total power. We can answer this question by finding
Coughlin&Begelman(2014)makearoughestimateof ǫ = 0.1, theminimumpossiblepowerforagivenprotonsynchrotronflux,
j
whichwealsoadopt.Then, M˙c2/L 103,i.e.,theaccretionis found todominate theoverall model spectra of theobjectsinthe
h Ei ∼
indeedhighlysupercritical.Theradiativeefficiencyoftheaccretion sample,seefig.9ofB13.WeusethemethodofZdziarski(2014)
discinthiscaseisverysmall, L /M˙c2 4 10 5. (hereafterZ14),whocalculatedtheminimumjetpowerforagiven
h acc i≃ × −
Afterthecalculationspresented inthispaper hadbeencom- electron synchrotron flux. Wecan adapt those calculations to the
pleted, Cerrutietal. (2015) presented an analysis of 5 high- proton synchrotron case by replacing the electron mass, m , by
e
frequencypeakedBLLacobjects(HBLs),whoseγ-raypeakislo- m intherelevantformulaeofZ14(includingphysicalconstants).
p
catedaround 1TeVratherthanat 1GeVastypicalforLBLsand Equivalently,σ ,thecriticalmagneticfield,B ,thedimensionless
∼ ∼ T cr
IBLsconsideredinB13andinthiswork.Cerrutietal.(2015)found photon energy in the jet frame, ǫ , and the jet-frame flux, L (in
thatitispossibletofindhadronic-modelfitswithsub-Eddingtonjet thenotationofZ14)needtobemu′ltipliedby(m /m ) 2,(m /m′ǫ′ )2,
p e − p e
powersforthoseparticularobjects.Adetailedanalysisofthoseob- (m /m ) 1 andm /m ,respectively.Correspondingly,theconstant
p e − p e
jects is outside the scope of this Letter, but we briefly address a a ofequation(33)ofZ14needstobemultipliedby(m /m )3/2,and
e p e
fewissues.Cerrutietal.(2015)tookintoaccountsecondaryprod- thepowerinrelativisticparticles,P ,andintherestmass,P,need
e i
uctsofhadronicprocessesinmoredetailthanB13.However,they tobemultipliedby(m /m )5/2andm /m ,respectively.Themini-
p e p e
assumedsteadystateprimaryprotonandelectrondistributionsas mumtotaljetpowerandthecorrespondingmagneticfieldstrength
fixed power laws and followed the evolution of particle spectra, ofequation(36) inZ14needtobemultipliedby(m /m )10/7 and
p e
usingtherespectivekineticequations,onlyforthesecondarypar- (m /m )5/7,respectively.
p e
ticles,whileB13usedtheelectronandprotonkineticequationsfor The method of Z14 assumes a local synchrotron spectrum
allparticles,whichistheself-consistentapproach.Itisnotclearto which can be well represented by a power law in some range of
ushowthismightaffectthejetpowers.Also,thejetpowersgiven frequencies, and it uses one monochromatic measurement of the
inCerrutietal.(2015)areforonejetonly,neglectthepressurecon- flux.Here,weuseanestimateofthefluxaroundthemaximumof
c 2015RAS,MNRAS000,1–6
(cid:13)
4 A. A. Zdziarski& M. Bo¨ttcher
4 ASTROPHYSICALIMPLICATIONS
0.0
PDB13 -0.2 Ionf BSe1c3tioexnce2e,dwtehefiorurnadditahtiavtethluemjeintopsoitwieesrsbyofvtehrey AlaGrgNe fsaacmtoprlse,
P(cid:144)est -0.4 withP/L 50–105 and P/L 3000.Then,weshowedin
@lg Sectionj 3atchca∼t thevalues ofhthjejaectcipo∼wer obtained byB13inthe
-0.6 a
hadronic model cannot be significantly reduced by changing the
-0.8 fitparameters,astheyare,onaverage,withinafactorofafewof
-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
lg@Lacc(cid:144)LED theminimumjetpowersestimatedusingtheobservedγ-rayspec-
tra for the radiative mechanism dominant in this model, namely
0.0
proton synchrotron. These findings imply that the jet formation
PDest -0.5 eisffiaclireenacdyygqrueiatetlyhiegxhce(esdees,the.agt.,foGuhnidseilnlinlieepttoanl.ic20m1o4d).elWs,ewhhaicvhe
(cid:144)min -1.0 alsofoundthatthemostefficientjetformationmechanismknown,
P
@lg based on the Blandford-Znajek mechanism extracting black-hole
-1.5
b spinwithamagneticallyarresteddisc(Tchekhovskoyetal.2011;
-2.0 McKinneyetal.2012),isruledoutbythemagneticfieldsmeasured
-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
atthepcdistancescale.Sincethejetpowerhastobethenderived
lg@Lacc(cid:144)LED entirelyfromaccretion,theimpliedaccretionratesarehugeandthe
Figure3.(a)Theratioofthetotaljetpowerestimatedusingthemagnetic radiativeefficienciesoftheaccretiondiscmustbetiny.
fieldstrengthsofB13andthemethodofZ14tothecorrespondingpower At the inferred accretion rates, M˙c2/L 103, accre-
giveninB13,asafunctionoftheEddingtonratio.Thedashedlinecorre- h Ei ∼
tionissupercritical(rulingoutoptically-thinradiativelyinefficient
spondstoequalpowers.(b)Theratiooftheminimumpowertothatcalcu-
models, which can correspond only to M˙c2/L 1, see, e.g.,
latedusingthemethodofZ14withthemagneticfieldstrengthsofB13.The E ≪
Yuan&Narayan 2014). The angle-averaged accretion-disc lumi-
dashedlinecorrespondstothegeometricaverage.
nosity in this case is small, corresponding to L L and a ra-
∼ E
diative efficiency is 10 3 (Sikora 1981; Sa¸dowskietal. 2014).
−
∼
However, most of that luminosity emerges through axial funnels,
wheretheobservedfluxissuper-Eddington,correspondingtoL
∼
10L (Sikora1981;Sa¸dowskietal.2014).Oursampleconsistsof
E
blazars seen close to on-axis, on average at i 1/Γ, and the
∼ j
accretion-disc-emission funnels have opening angles greater than
theνF spectrum,usingspectralplotsinfig.9ofB13.Welistour
ν that (Sa¸dowskietal. 2014). Thus, we would expect to see super-
adoptedvaluesinTable1.Thisimpliesthattheparametere of
max Eddington accretion-disc luminosities, while, in fact, they are all
Z14is= 1.However,wemodifythemethodinordertotakeinto < L , with 8 out of 12 objects having L < 0.1L . Thus, the
E acc E
accountthatγminisspecifiedinthemodelofB13.Inthecaseofion h∼adronicemissionmodelforthejetsisincons∼istentwiththestan-
acceleration,onewouldnaturallyexpectγ 1,unlikethecase
min ∼ dardaccretiontheory.
ofelectrons,whichcanbepreheatedto γ 1(withacceler-
h mini ≫ The inferred extreme accretion rates present also a major
ationonlyproceedingoutofthisdistribution).However,B13used
γ = 103 forsomeobjects,seeTable1.Toaccount forthis,we problem in light of results of studies of supermassive-black-hole
min
definee =Bγ2 /(B m2ǫ )(cf.Z14).SinceBisitselfcalculated growth. The e-folding time by which the black-mass would in-
min min cr p ′ creaseduetoaccretion, M/M˙,is 4 105 yrat M˙c2/L 103
bytheminimization,thisrequiresasimpleiterativecalculation. ≃ × h Ei ≃
foundinSection2.Thisisaveryshorttimecomparedtoestimated
Wefirstcheckhowwelltheabovemethodreproducesthejet
lifetimesofactivephasesofradiosources,e.g., 2 108yrforFR
powersgiveninB13.Forthis,weusethevaluesofBgiveninB13 ≃ ×
IIs(Antognini,Bird&Martini 2012andreferences therein).Cor-
instead of those corresponding to the minimum power. We show
respondingly, the average radiative accretion efficiency we found
theresultsinFig.3(a).Somedisagreementisexpectedgiventhat
(undertheassumptionsofthehadronicmodel)of L /M˙c2 4
inthepresent estimatewetake intoaccount onlytheproton syn- h acc i≃ ×
10 5is thantheaverageaccretionefficiencyof 0.1–0.3(Sołtan
chrotronemissionandneglectcooling.Theadiabaticcoolingis,in − ≪ ∼
1982; Marconietal. 2004; Silvermanetal. 2008; Schulzeetal.
fact,dominantinAO0235+164andWComae,inwhichcasethe
2015). Thus, blazars radiating via the hadronic emission mecha-
proton-synchrotron estimate gives values 200 and 50 times too
∼ nismhavetorepresentatmostasmallfractionofaccretingsuper-
low, respectively. Apart from this, the overall agreement isgood,
massiveblackholesand/or suchextremeaccretionepisodesmust
withinafactorof2for7fortheremainingobjects,seeFig.3(a).
be extremely short-lived, representing only a duty-cycle of order
WethenapplytheminimizationmethodtothesampleofB13.
10 4 (whichisinconflict withthefact that thestudied objects
We have found the minimum powers are on average lower by a ∼ −
havequiteaverageproperties).
factoroffewcomparedtothecorrespondingestimatesabove,with
thegeometricaveragebeing 0.23,seeFig.3(b).Thisreduction Finally, the obtained extreme powers are in conflict
≃
isduetotheminimumcorresponding toanequipartitionbetween with studies of the jet power based on radio lobes and
thepowerintherelativisticions,P,andinthemagneticfield,P , X-ray cavities (Merloni&Heinz 2007; Cavagnoloetal. 2010;
i B
whichmaynotbeabletoproduceafittotheentireSED.Indeed, Nemmenetal.2012;Russelletal.2013;Godfrey&Shabala2013;
B13 found P P in most of their fits. This departure from Shabala&Godfrey 2013). Those studies indicate jet powers at
i ≫ B
equipartition naturally resultsinhigher total jet powers. Still,the mostmoderatelyexceedingtheEddingtonluminosity,andevenin
overallpossiblereductionofthejetpowerduetochangingthefit themostluminoussourcestheyexceedtheaccretion-discluminos-
parametersisbyatmostafactorofafew. ityonlybyafactorof<10.Ontheotherhand,thosepowersarein
∼
c 2015RAS,MNRAS000,1–6
(cid:13)
Hadronicmodelsof blazars 5
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ACKNOWLEDGEMENTS
ValtonenM.J.,CipriniS.,LehtoH.J.,2012,MNRAS,427,77
WethankMarekSikoraforvaluablediscussions,andPatrykPjanka WangJ.-M.,LuoB.,HoL.C.,2004,ApJ,615,L9
for help withthe dataanalysis. Thisresearch has been supported XieZ.H.,HaoJ.M.,DuL.M.,ZhangX.,JiaZ.L.,2008,PASP,
in part by the Polish NCN grants 2012/04/M/ST9/00780 and 120,477
2013/10/M/ST9/00729. MBacknowledgessupportbytheDepart- YuanF.,NarayanR.,2014,ARA&A,52,529
mentofScienceandTechnologyandtheNationalResearchFoun- Zamaninasab M., Clausen-Brown E., Savolainen T.,
dationoftheRepublicofSouthAfricathroughtheSouthAfrican TchekhovskoyA.,2014,Nature,510,126(ZCST14)
ResearchChairInitiative(SARChI). ZdziarskiA.A.,2014,MNRAS,445,1321(Z14)
c 2015RAS,MNRAS000,1–6
(cid:13)
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c 2015RAS,MNRAS000,1–6
(cid:13)